**TI 84 Plus CE: Nested Square Root Sums**

**Introduction**

The program NESTSQM calculates the sequence:

√(a + b)

√(a + b * √(a + b))

√(a + b * √(a + b * √(a + b))

√(a + b * √(a + b * √(a + b * √(a + b)))

...

√(a + b * √(a + b * ... * √(a + b)))

In other words, start with c = 1.

Then let c = √(a + b * c)

Repeat.

The calculation is shown in steps of 5, for a total of 25 steps.

**TI-84 Plus CE Program: NESTSQSM**

"2020-01-05 EWS"

Disp "√(A+B√(A+B√(A+B...","25 ITERATIONS","TI-84+ CE"

Prompt A,B

1→C

For(K,1,25)

√(A+B*C)→C

Disp C

If fPart(K/5)=0

Then

Disp " "

Disp toString(K-4)+" TO "+toString(K)

Pause

ClrHome

End

End

**Examples**

Example 1: a = 2, b = 3

2.236067977

2.95096661

3.294373966

3.447190436

3.513057259

3.541069299

3.552915408

3.557913184

3.5600196

3.560907019

3.561280817

3.561438256

3.561504565

3.561532493

3.561544255

3.561549208

3.561551295

3.561552173

3.561552544

3.561552699

3.561552765

3.561552793

3.561552804

3.561552809

3.561552811

Example 2: a = 7, b = 4

3.31662479

4.501832867

5.000733093

5.196434583

5.271217917

5.299516173

5.310184996

5.314201726

5.315713207

5.316281861

5.316495786

5.316576262

5.316606535

5.316617923

5.316622207

5.316623819

5.316624425

5.316624653

5.316624739

5.316624771

5.316624783

5.316624788

5.316624789

5.31662479

5.31662479

Eddie

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